Continuously variable torque transfer mechanism

ABSTRACT

A transmission for transferring torque from a prime mover includes a first input shaft adapted to be driven by the prime mover, a second input shaft, an output shaft and an epicyclic gearset. The gearset includes a ring gear being driven by the first input shaft, pinion gears being driven by the ring gear, a sun gear driven by the second input shaft and driving the pinion gears, and a carrier driving the output shaft. A reaction motor drives the second input shaft. A controller controls the reaction motor to vary the speed of the second input shaft and define a gear ratio between the first input shaft and the output shaft based on the second input shaft speed.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.12/766,954 filed Apr. 26, 2010 which is a continuation-in-part of U.S.patent application Ser. No. 12/617,031 filed on Nov. 12, 2009. Theentire disclosure of each of the above applications is incorporatedherein by reference.

FIELD

The present disclosure relates to power transmission devices. Moreparticularly, a transmission for transferring torque at a variable speedreduction ratio includes a planetary gear drive driven by two sources ofpower.

BACKGROUND

Geared transmissions typically function to change the rotational speedof a prime mover output shaft and an input shaft of a desired workoutput. In a vehicle, the prime mover may include a diesel or gasolineinternal combustion engine. It should be noted that there are many moreapplications than automobiles and trucks. Locomotives are equipped withtransmissions between their engines and their wheels. Bicycles andmotorcycles also include a transmission. Speed-increasing transmissionsallow the large, slow-moving blades of a windmill to generate power muchcloser to a desired AC frequency. Other industrial applications exist.In each case, the motor and transmission act together to provide powerat a desired speed and torque to do useful work. Geared transmissionshave also been used in combination with electric motors acting as theprime mover.

Multiple speed transmissions have been coupled to high torque primemovers that typically operate within a narrow speed range, most notablystructured as large displacement diesel engines of tractor trailers.Electric motors have a much wider speed range in which they operateeffectively. However, the motor operates most efficiently at a singlespeed. Known multiple speed transmissions attempt to maintain an optimumoperating speed and torque of the prime mover output shaft, but onlyapproach this condition due to the discrete gear ratios provided.Accordingly, a need for a simplified variable speed ratio powertransmission device exists.

Many existing transmissions incorporate planetary gearsets within thetorque path. A traditional planetary gear drive has three majorcomponents: a sun gear, an annulus ring gear and a planet carrier. Whenone of those components is connected to the prime mover, another is usedas the output and the third component is not allowed to rotate, theinput and output rotate at different speeds, and may also rotate inopposite directions, with the ratio of input to output speeds being afixed value. If the previously fixed third component is connected to asecond input and forced to rotate, the transmission will have acontinuously varying speed ratio dependent on the speeds of both theprime mover and this new second input. One example of such a planetarygear drive is made by Toyota. While planetary gearsets have beensuccessfully used in vehicle power transmissions in the past, a needexists for a planetary drive and control system for optimizing the geardrive's efficiency and power density.

SUMMARY

This section provides a general summary of the disclosure, and is not acomprehensive disclosure of its full scope or all of its features.

A transmission for transferring torque from a prime mover includes afirst input shaft adapted to be driven by the prime mover, a secondinput shaft and an output shaft. A compound planetary gearset includes asun gear driven by the first input shaft, first pinion gears beingdriven by the sun gear, a ring gear fixed for rotation with the secondinput shaft and being meshed with second pinion gears, and a carrierdriving the output shaft. A reaction motor drives the second inputshaft. A controller controls the reaction motor to vary the speed of thesecond input shaft and define a gear ratio between the first input shaftand the output shaft based on the second input shaft speed.

A transmission for transferring torque from a prime mover includes afirst input shaft adapted to be driven by the prime mover, a secondinput shaft, an output shaft and an epicyclic gearset. The gearsetincludes a ring gear being driven by the first input shaft, pinion gearsbeing driven by the ring gear, a sun gear driven by the second inputshaft and driving the pinion gears, and a carrier driving the outputshaft. A reaction motor drives the second input shaft. A controllercontrols the reaction motor to vary the speed of the second input shaftand define a gear ratio between the first input shaft and the outputshaft based on the second input shaft speed.

A transmission includes a first input shaft adapted to be driven by theprime mover, a second input shaft, an output shaft, and an epicyclicgearset. The gearset includes a sun gear being driven by the first inputshaft, pinion gears in meshed engagement with the sun gear, a carrierdriven by the second input shaft and rotatably supporting the piniongears, and a ring gear fixed for rotation with the output shaft. Areaction motor drives the second input shaft. A controller controls thereaction motor to vary the speed of the second input shaft and define agear ratio between the first input and the output shaft based on the asecond input shaft speed.

Further areas of applicability will become apparent from the descriptionprovided herein. The description and specific examples in this summaryare intended for purposes of illustration only and are not intended tolimit the scope of the present disclosure.

DRAWINGS

The drawings described herein are for illustrative purposes only ofselected embodiments and not all possible implementations, and are notintended to limit the scope of the present disclosure.

FIG. 1 is a schematic depicting an exemplary vehicle equipped with atransmission constructed in accordance with the teachings of the presentdisclosure;

FIG. 2 is a schematic representation of a transmission having a simpleplanetary gearset;

FIG. 3 is a graph depicting sun speed to carrier speed ratio versus ringspeed to sun speed ratio for a number of fixed ring ratios of a simpleplanetary gearset;

FIG. 4 depicts relative diameters of sun, planet and annulus ring gearsfor a planetary gearset having a fixed ring ratio of 9.706.

FIG. 5 is a schematic depicting a transmission equipped with a compoundplanetary gearset;

FIG. 6 is a graph depicting sun speed to carrier speed ratio versus ringspeed to sun speed ratio for a number of compound planetary gearsets;

FIG. 7 is a schematic of an alternate transmission including a simpleplanetary gearset and an offset motor and speed reduction unit;

FIG. 8 is a schematic depicting another transmission having a compoundplanetary gearset driven by an offset reaction motor and speed reductionunit;

FIG. 9 is a schematic of another transmission including two simpleplanetary gearsets;

FIG. 10 is a schematic of another transmission equipped with a compoundplanetary gearset and a simple planetary reduction gearset;

FIGS. 11 and 12 depict alternate transmissions including worm and wormwheel drives;

FIGS. 13 and 14 depict alternative transmissions includingconcentrically arranged worm drive mechanisms;

FIG. 15 is a schematic representation of a transmission having a simplesolar epicyclic gearset;

FIG. 16 is a graph depicting ring speed to carrier speed ratio versussun speed to ring speed ratio for a number of fixed sun speed ratios ofa simple solar epicyclic gearset;

FIG. 17 is a schematic representation of a transmission having a simplestar epicyclic gearset;

FIG. 18 is a graph depicting carrier speed to ring speed ratio versussun speed to ring speed ratio for a number of fixed sun speed ratios ofa simple star epicyclic gearset;

FIG. 19 is a graph depicting speed ratio sensitivity versus ring speedfor a compound solar epicyclic gearset; and

FIG. 20 is a graph depicting speed ratio sensitivity versus carrierspeed for a compound star epicyclic gearset.

Corresponding reference numerals indicate corresponding parts throughoutthe several views of the drawings.

DETAILED DESCRIPTION

The present disclosure is directed to a transmission that can beadaptively controlled to transfer torque between a first rotary memberand a second rotary member. The transmission finds particularapplication in motor vehicle drivelines such as, for example, acontinuously variable torque transfer mechanism. Thus, while thetransmission of the present disclosure is hereinafter described inassociation with particular arrangements for use in specific drivelineapplications, it will be understood that the arrangements shown anddescribed are merely intended to illustrate embodiments of the presentdisclosure.

With particular reference to FIG. 1 of the drawings, a drivetrain 10 foran all-wheel drive vehicle is shown. Drivetrain 10 includes a driveline12 and a powertrain 16 for delivering rotary tractive power (i.e., drivetorque) to the driveline. In the particular arrangement shown, driveline12 is the rear driveline. Powertrain 16 is shown to include an engine 18and a transmission 20. A pair of front wheels 24L and 24R are notdriven. Driveline 12 includes a propshaft 30 driven by transmission 20and a rear axle assembly 32 for transferring drive torque from engine 18to a rear differential 34. A pair of rear axleshafts 38L and 38Rinterconnect rear differential 34 to corresponding rear wheels 36L and36R.

As shown in FIGS. 1 and 2, transmission 20 includes a planetary gearset40 and a reaction motor 42. Drivetrain 10 is shown to further includevehicle sensors 44 for detecting certain dynamic and operationalcharacteristics of the motor vehicle and a controller 45 for controllingactuation of reaction motor 42 in response to input signals from vehiclesensors 44.

Planetary gearset 40 includes a sun gear 46 fixed for rotation with anoutput shaft 48 of engine 18. An annulus ring gear 50 is fixed forrotation with an output shaft 52 of reaction motor 42. Planetary gearset40 also includes a carrier 54 rotatably supporting a plurality of piniongears 56 that are each in constant meshed engagement with annulus ringgear 50 and sun gear 46. An output shaft 58 is fixed for rotation withcarrier 54. The remainder of this disclosure discusses how the sun gearspeed ω_(S) to carrier speed ω_(C) ratio is a function of an annulusring gear speed ω_(R) to sun speed ratio in simple and compoundplanetary gearsets and how the asymptotic nature of this speed ratio maybe exploited to improve the gear drive's efficiency and power density.

If a positive direction of annulus ring rotation is defined to be in thesame direction as that of the sun gear and carrier assembly, it can beshown that in the general case, the ratio of sun to carrier speeds isgiven by:

$\begin{matrix}{\frac{\omega_{S}}{\omega_{C}} = {\frac{z_{S} + z_{R}}{z_{S}}\left\lbrack {1 - \left( \frac{\omega_{R}z_{R}}{{\omega_{S}z_{S}} + {\omega_{R}z_{R}}} \right)} \right\rbrack}} & (1)\end{matrix}$

where ω_(S), ω_(C), and ω_(R) are the sun, carrier and annulus ringangular velocities and z_(R) and z_(S) are the number of teeth in theannulus ring and sun gears, respectively. Note that if ω_(R)=0, equation(1) simplifies to the familiar relationship between sun and carrierspeeds for a fixed annulus ring.

We define the ratio of ring speed to sun speed as

$\begin{matrix}{\omega_{R\text{/}S} = \frac{\omega_{R}}{\omega_{S}}} & (2)\end{matrix}$

Equation (1) may then be rewritten as

$\begin{matrix}{\frac{\omega_{S}}{\omega_{C}} = \frac{z_{R} + z_{S}}{z_{S} + {\omega_{R\text{/}S} \cdot z_{R}}}} & (3)\end{matrix}$

It can be noted that there will be a value of ω_(R/S) for whichω_(S)/ω_(C) will become asymptotic. FIG. 3 shows equation (3) plottedagainst the ring to sun speed ratio for different numbers of ring andsun gear teeth. Each curve is labeled with its carrier to sun fixed ringratio (FRR). Table 1 lists the number of teeth in the sun, planets andring of each planetary combination, as well as each tooth combination'sFRR. The combinations of sun, planet and ring gear tooth numbers wereselected to span the practical limits of geometry constraints.

FIG. 3 plots the speed ratio ω_(S)/ω_(C) against ω_(R/S) for various FRRvalues listed in Table 1 and shows that the vertical asymptote increasesfrom ω_(R/S)=−0.650 to −0.115 as the FRR increases. More importantly,the magnitude of the ω_(S)/ω_(C) slope as the curve crosses the ordinateaxis ω_(R/S)=0 increases as well. As the magnitude of the ω_(S)/ω_(C)slope increases, the annulus ring speed required to effect a change inthe speed ratio ω_(S)/ω_(C) decreases dramatically. The annulus ringgear 50, however, is the largest of all component gears in the planetarygearset 40. As such, a relatively large torque may need to be reacted byreaction motor 42. The torque necessary to supply a sufficient reactionto pinion gears 56 may be quite large as well.

The sensitivity of the speed ratio to its fixed ring ratio is quantifiedby defining the ratio of the highest to lowest speed ratios as Δ for anarbitrary value of ω_(R/S) selected as +/−10% of the sun's speed, aswell as the value of ω_(R/S) for the vertical asymptote. Table 1presents this data.

TABLE 1 Simple Planetary Tooth Combinations Ratio Spread Numbers ofTeeth Fixed Ring Δ = (ω_(S)/ω_(C))_(MAX)/ Vertical Sun Planets RingSpeed Ratio (ω_(S)/ω_(C))_(MIN) Asypmptote z_(S) z_(P) z_(R) (z_(S) +z_(R))/z_(S) −0.1 < ω_(R/S) < 0.1 ω_(R/S) = ω_(R)/ω_(S) 17 65 148 9.70614.455 −0.115 20 62 145 8.250 6.273 −0.138 23 59 142 7.174 4.227 −0.16228 54 137 5.893 2.916 −0.204 34 48 131 4.853 2.254 −0.260 41 41 1244.024 1.867 −0.331 52 30 113 3.173 1.555 −0.460 65 17 100 2.538 1.364−0.650

Table 1 and FIG. 3 illustrate that a large fixed ring ratio (FRR) isnecessary to have the desirable feature of ω_(S)/ω_(C) speed ratiosensitivity. Design constraints may exist where such a large FRR is notpractical. FIG. 4 shows the relative diameters of the sun, planets andannulus ring of the 9.706 FRR planetary. The relatively small sun sizewill limit the strength of the shaft on which the sun gear is fixed.Furthermore, just as there is a minimum practical FRR, below which theplanet pinions are too small to be supported with rolling elementbearings, there is a maximum FRR, above which the tips of the planetpinions will interfere.

FIG. 5 depicts an alternative transmission 20 a having a compoundplanetary gearset 40 a in lieu of simple planetary gearset 40.Alternative transmission 20 a is substantially similar to transmission20. Accordingly, like elements will be identified with referencenumerals including an “a” suffix. Planetary gearset 40 a differs fromsimple planetary gearset 40 in that compound pinion gears 60 replacepinion gears 56. Each compound pinion gear 60 includes a first piniongear 62 in meshed engagement with sun gear 46 a as well as a reduceddiameter second pinion gear 64 in constant meshed engagement withannulus ring gear 50 a. First pinion gears 62 have a predeterminednumber of teeth, module, pressure angle and helix angle based on themesh with sun gear 46 a. Second pinion gears 64 have a reduced number ofteeth, a different module, pressure angle and helix angle for the gearmeshes with annulus ring gear 50 a. The compound planetary gearsetprovides a minimized inner and outer radial packaging. Furthermore, thecompound planetary gearset provides a greater reduction gear ratio. Itshould be appreciated that first pinion gears 62 and second pinion gears64 are aligned in pairs to rotate on common pinion centers.

To operate on the same pinion centers, the module, helix angle andnumber of teeth must satisfy this constraint:

$\begin{matrix}{\frac{m_{R}\mspace{14mu} \cos \mspace{14mu} \beta_{S}}{m_{S}\mspace{14mu} \cos \mspace{14mu} \beta_{R}} = \frac{z_{S} + z_{PS}}{z_{R} - z_{PR}}} & (4)\end{matrix}$

where m_(R) and m_(S) are the normal modules of the ring and sun meshes,respectively. The planet pinions z_(PS) and z_(PR) mesh with the sun andannulus, respectively. In addition to the geometry constraint ofequation (4), each of the compound planet pinions independent meshesmust have the same torque, but because each torque will act at differentpitch geometries, the tooth loads may differ significantly and requirelargely different modules as a result.

If the design of a compound planetary gear set is modified to allow foran annulus gear that may move at a controlled angular speed while stillproviding the necessary reaction torque for the planet pinions, asimilar asymptotic behavior to that seen in FIG. 3 exists. With the samereasoning used to develop equations (1) and (2), it can be shown thatthe speed ratio ω_(S)/ω_(C) of a compound planetary gear set, in whichthe annulus gear is allowed to rotate is given by:

$\begin{matrix}{\frac{\omega_{S}}{\omega_{C}} = \frac{{z_{R} \cdot z_{PS}} + {z_{S} \cdot z_{PR}}}{{z_{S} \cdot z_{PR}} + {\omega_{R\text{/}S} \cdot z_{R} \cdot z_{PS}}}} & (5)\end{matrix}$

As with equations (1) and (2), equation (5) reduces to the familiarspeed relationship for a fixed annulus ring when ω_(R/S)=0. Since acompound planetary gear set is capable for a larger speed ratioω_(S)/ω_(C), the benefits of the asymptotic nature of equation (5) canbe more fully exploited. FIG. 6 shows the sun-carrier speed ratios againplotted against ring-sun speed ratios for different fixed ring ratios.

TABLE 2 Compound Planetary Tooth Combinations Numbers of Teeth FixedRing Ratio Spread Planets Planets Speed Ratio Δ = (ω_(S)/ω_(C))_(MAX)/Sun (Sun) (Ring) Ring (z_(S)z_(PR) + z_(R)z_(PS))/ (ω_(S)/ω_(C))_(MIN)z_(S) z_(PS) z_(PR) z_(R) (z_(S)z_(PR)) −0.03 < ω_(R/S) < 0.03 19 79 17115 29.127 11.805 22 79 17 115 25.291 6.373 23 76 17 98 20.049 3.667 2968 17 100 14.793 2.412 35 64 19 94 10.047 1.745 37 50 23 107 7.287 1.46547 46 23 95 5.043 1.276

As was done for simple planetary gear drives, tooth combinations shownin Table 2 were selected to attempt to span the practical FRR limits. AFRR less than 5.043 would most likely not justify the additionalcomplexity and expense of a compound planetary over a simple planetaryand a FRR larger than 30 may not be practical, as can be seen from FIG.6. It is also noted that in comparing FIGS. 3 and 6, it can be seen fora given FRR a compound planetary will have a larger asymptote value thana simple planetary.

FIG. 7 depicts an alternate transmission 20 b and is constructedsubstantially similarly to transmission 20. Similar elements will beidentified with like reference numerals including a “b” suffix. Areaction motor 42 b includes an output shaft 52 b that extends offsetand parallel to an axis of rotation of output shaft 58 b. Reaction motor42 b drives a reduction gearset 72 to rotate ring gear 50 b. Reductiongearset 72 includes a first gear 76 fixed for rotation with output shaft52 b. A second gear 78 is in constant meshed engagement with first gear76 and is fixed for rotation with a concentric shaft 80. Annulus ringgear 50 b is also fixed for rotation with concentric shaft 80.

FIG. 8 depicts an alternate transmission identified at reference numeral20 c. Transmission 20 c includes the offset motor and speed reductionunit arrangement shown in FIG. 7 being used in conjunction with thecompound planetary gearset first described at FIG. 5. Accordingly,similar elements will be identified with like reference numeralsincluding a “c” suffix. In operation, reaction motor 42 c drives firstgear 76 c and second gear 78 c to rotate annulus ring gear 50 c and varythe output ratio provided to output shaft 58 c.

FIG. 9 depicts another alternate transmission identified at referencenumeral 20 d. Transmission 20 d is substantially similar to transmission20 with the addition of a planetary reduction gearset 90. Similarelements will be identified with like reference numerals having a “d”suffix. Planetary gearset 90 includes a sun gear 92 fixed for rotationwith reaction motor output shaft 52 d. Reaction motor output shaft 52 dis concentrically aligned with and circumscribes output shaft 58 d. Aring gear 94 is restricted from rotation. A plurality of pinion gears 96are supported for rotation on a carrier 98. Pinion gears 96 are eachmeshed with sun gear 92 and ring gear 94. Carrier 98 is fixed forrotation with a concentric shaft 100. Annulus ring gear 50 d is alsofixed for rotation with concentric shaft 100.

FIG. 10 depicts another alternate transmission 20 e that incorporatesthe planetary reduction gearset of FIG. 9 and mates it with the compoundplanetary gear arrangement shown in FIG. 5. Similar elements will beidentified with like reference numerals having a “e” suffix. Reactionmotor 42 e includes an output shaft 52 e transferring torque toplanetary reduction unit 90 e. Carrier 98 e is fixed for rotation withconcentric shaft 100 e and annulus ring gear 50 e.

FIGS. 11 and 12 depict alternate transmissions 20 f and 20 g,respectively. Each of transmissions 20 f, 20 g include a worm drive 110including a reaction motor 42 f, 42 g, driving a worm gear 112 along anaxis of rotation that extends substantially perpendicular to an axis ofrotation of output shaft 58 f, 58 g. Worm gear 112 is in constant meshedengagement with a worm wheel 114. Worm wheel 114 is fixed for rotationwith a concentric shaft 116. In FIG. 11, concentric shaft 116 is fixedfor rotation with annulus ring gear 50 f. In similar fashion, concentricshaft 116 of FIG. 12 is fixed for rotation with annulus ring gear 50 g.

FIGS. 13 and 14 also depict alternative transmissions identified atreference numerals 20 h and 20 i, respectively. FIGS. 13 and 14 aresubstantially similar to FIGS. 11 and 12 except that worm wheels 114 h,114 i concentrically surround annular ring gears 50 h and 50 i.

FIG. 15 depicts a solar epicyclic gear arrangement 120 defined by sungear 46, annulus ring gear 50, carrier 54, pinion gears 56 and reactionmotor 42 when output shaft 52 of reaction motor 42 is fixed for rotationwith sun gear 46. Engine 18 acts as the prime mover supplying torque todriveline 12. Output shaft 58 is fixed to carrier 54. Since the reactionmember of a solar arrangement is sun gear 46, we define the sun gear'sspeed in terms of annulus ring gear 50:

ω_(S)=ω_(S/R)·ω_(R)  (6)

The input to output speed ratio u may be expressed as:

$\begin{matrix}{u = {\frac{\omega_{R}}{\omega_{C}} = \frac{z_{S} + z_{R}}{z_{R} + {\omega_{S\text{/}R} \cdot z_{S}}}}} & (7)\end{matrix}$

At FIG. 16, we plot the above equation for the same sun, planet andannulus ring tooth combinations in an attempt to span the limits ofpracticality. For simplicity, the same sun, planet and ring toothcombinations used for planetary arrangements are used again for solararrangements. Note that both the scale and the fixed ring ratios havebeen updated to agree with the above equation, but the generalasymptotic nature is the same as FIG. 3. However, the sun-to-ring speedratios at which the vertical asymptotes exist are observed to occur atdifferent values.

As was with planetary gearset 40, the power and steady-state torque intothe gear drive must balance that exiting the gear drive.

τ_(R)+τ_(S)=τ_(C)  (8)

τ_(R)·ω_(R)+τ_(S)·ω_(S)=τ_(C)·ω_(C)  (9)

As before, we make the kinematics and steady-state torque substitutionsinto the power balance equation, and obtain the carrier and sun torquesin terms of the ring torque.

$\begin{matrix}{\frac{\tau_{C}}{\tau_{R}} = \frac{z_{S} + z_{R}}{z_{R}}} & (10) \\{\frac{\tau_{S}}{\tau_{R}} = \frac{z_{S}}{z_{R}}} & (11)\end{matrix}$

As was done in the previous section with planetary gearset 40, we againdefine the ratio of the reaction power to the input power as and writethat for the solar arrangement variable speed ratio,

$\begin{matrix}{u = {\frac{z_{S} + z_{R}}{z_{R} + {\omega_{S\text{/}R} \cdot z_{S}}} = \frac{z_{S} + z_{R}}{z_{R}\left( {1 + \kappa} \right)}}} & (12)\end{matrix}$

The same relationship for transmission ratio spread as was discussedearlier exists as well. Therefore, for both a planetary and solarepicyclic arrangement, the kinematics exhibits an asymptotic behavior.However, the speeds of the reaction member at which the asymptote isobserved will depend on the type of epicyclic arrangement, as well asthe fixed reaction member speed ratios. In both cases, the transmissionratio spread required for the application will define the powerrequirements of the reaction motor/generator.

Another alternate transmission is shown in FIG. 17 and identified as astar epicyclic gear arrangement having each of sun gear 46, annulus ringgear 50, carrier 54, pinion gears 56 and reaction motor 42. Prime moveror engine 18 drives sun gear 46. Reaction motor 42 drives carrier 54.Output shaft 58 is fixed to annulus ring gear 50. As with the planetaryand solar epicyclic gear drives, we define the reaction member's speedin terms of the input's. For a star gear drive, the reaction member isthe carrier.

ω_(C)=ω_(C/S)·ω_(S)  (13)

If we follow the same steps as we did for the planetary and solarepicyclic gear drives, we can rearrange the equation to give us the sunto ring speed ratio.

$\begin{matrix}{u = {\frac{\omega_{S}}{\omega_{R}} = \frac{- z_{R}}{z_{S} - {\omega_{C\text{/}S} \cdot \left( {z_{S} + z_{R}} \right)}}}} & (14)\end{matrix}$

Note that the negative sign in front of the right hand side means theinput and output shafts will rotate in opposite directions when thecarrier speed is zero. FIG. 18 plots the speed ratio against ω_(C/S).

τ_(S)−τ_(C)=−τ_(R)  (15)

τ_(S)·ω_(S)−τ_(C)·ω_(C)=τ_(R)·ω_(R)  (16)

After substitute and rearranging terms of the above equations, the ringand carrier torques may be expressed in terms of the sun torque. Thering and carrier torques must be in a direction opposite to that of thesun. This has been addressed with the negative signs in the equationabove.

$\begin{matrix}{\frac{\tau_{R}}{\tau_{S}} = \frac{- z_{R}}{z_{S}}} & (17) \\{\frac{\tau_{C}}{\tau_{S}} = \frac{- \left( {z_{S} + z_{R}} \right)}{z_{S}}} & (18)\end{matrix}$

The ratio of the reactive power to the input power as defined as κ.However, since the carrier and sun torques are in opposite directions,the same will be true of their powers. Therefore, when the carrier andsun speeds are in the same direction κ.<0, and when the carrier and sunare in opposite directions, κ.>0 and we have as was true for theplanetary and solar arrangements:

$\begin{matrix}{u = {\frac{- z_{R}}{z_{S}\left( {1 + \kappa} \right)} = \frac{u_{F}}{\left( {1 + \kappa} \right)}}} & (19)\end{matrix}$

Thus, in all three epicyclic arrangements, when it is desirable to havea greater speed reduction than the fixed reaction-member ratio, thedevice that powers the input member must also power the reaction deviceto provide this additional speed reduction ratio. Conversely, if it isdesired to have a speed reduction ratio that is less than that of thefixed reaction-member ratio, the reaction device must power the reactionmember to achieve this kinematic relationship. The reaction power willexit the gear drive through the output member, adding to the poweroutput of the gear drive.

It should be appreciated that solar gear arrangement 120 and star geararrangement 150 may be modified to function with compound planet gearsas previously described in relation to FIG. 5. The offset drive andspeed reduction units of FIGS. 7-14 may also be used with the solar andstar simple or compound epicyclic gearset arrangements.

The kinematics relationships for the compound solar and star epicyclicarrangements are derived in a manner similar to that previouslydescribed. FIGS. 19 and 20 show the speed reduction ratios plottedagainst the ratio of the reaction member to input member speed forcompound solar and star arrangements, respectively. It should be notedthat the fixed ring speed ratios of the compound solar epicyclicgearsets range between 1.03 and 1.25. Furthermore, the verticalasymptote of a ratio of carrier speed to sun gear speed versus a ratioof sun gear speed to ring gear speed for the compound solar gearsetranges between 5 and 28.

Regarding FIG. 20 and the star epicyclic gearsets, the fixed carrierspeed ratios of the compound star epicyclic gearsets range between −4.0and 28.0. The vertical asymptote of a ratio of ring gear speed to sungear speed versus a ratio of carrier speed to sun gear speed ranges forthe compound solar gearsets between 0.02 and 0.20. The planetary, solarand star arrangement speed reduction ratios can be simplified using thereactive power quotients and, as with their simple epicycliccounterparts, can all be written as the fixed reaction member speedratio divided by the quantity 1+κ.

Tables 3, 4 and 5 summarize the speed reduction ratios and planetspeeds, torque and power for each epicyclic gear drive considered. Table6 summarizes the speed reduction ratios using the reactive powerquotients for each arrangement and Table 7 summarizes the asymptoticcharacteristics of where the asymptote occurs and what is the slope asthe curve crosses the vertical axis.

TABLE 3 Speed Reduction Ratio and Planet Speeds SPEED REDUCTION RATIOPLANET SPEEDS Simple Planetary$\frac{\omega_{S}}{\omega_{C}} = \frac{z_{R} + z_{S}}{z_{S} + {\omega_{R/S} \cdot z_{R}}}$$\frac{\omega_{P}}{\omega_{S}} = \frac{\left( {\omega_{R/S} \cdot z_{R}} \right) - z_{S}}{2 \cdot z_{P}}$Compound Planetary$\frac{\omega_{S}}{\omega_{C}} = \frac{{z_{R} \cdot z_{PS}} + {z_{S} \cdot z_{PR}}}{{z_{S} \cdot z_{PR}} + {\omega_{R/S} \cdot z_{R} \cdot z_{PS}}}$$\frac{\omega_{P}}{\omega_{S}} = \frac{\left( {\omega_{R/S} \cdot z_{R} \cdot z_{PS}} \right) - {z_{S} \cdot z_{PR}}}{2 \cdot z_{PR} \cdot z_{PS}}$Simple Solar$\frac{\omega_{R}}{\omega_{C}} = \frac{z_{R} + z_{S}}{z_{R} + {\omega_{S/R} \cdot z_{S}}}$$\frac{\omega_{P}}{\omega_{R}} = \frac{z_{R} - \left( {z_{S} \cdot \omega_{S/R}} \right)}{2 \cdot z_{P}}$Compound Solar$\frac{\omega_{R}}{\omega_{C}} = \frac{{z_{R} \cdot z_{PS}} + {z_{S} \cdot z_{PR}}}{{z_{R} \cdot z_{PS}} + {\omega_{S/R} \cdot z_{S} \cdot z_{PR}}}$$\frac{\omega_{P}}{\omega_{R}} = \frac{{z_{R} \cdot z_{PS}} - \left( {\omega_{R/S} \cdot z_{S} \cdot z_{PR}} \right)}{2 \cdot z_{PR} \cdot z_{PS}}$Simple Star$\frac{\omega_{R}}{\omega_{S}} = \frac{- z_{R}}{z_{S} - {\omega_{C/S} \cdot \left( {z_{R} + z_{S}} \right)}}$$\frac{\omega_{P}}{\omega_{S}} = \frac{\left\lbrack {\omega_{C/S} \cdot \left( {z_{R} + z_{S}} \right)} \right\rbrack - z_{S}}{2 \cdot z_{P}}$Compound Star$\frac{\omega_{R}}{\omega_{S}} = \frac{{- z_{R}} \cdot z_{PS}}{{z_{S} \cdot z_{PR}} - {\omega_{C/S} \cdot \left( {{z_{R} \cdot z_{PS}} + {z_{S} \cdot z_{PR}}} \right)}}$$\frac{\omega_{P}}{\omega_{S}} = \frac{\left\lbrack {\omega_{C/S} \cdot \left( {{z_{R} \cdot z_{PS}} + {z_{S} \cdot z_{PR}}} \right)} \right\rbrack - {z_{S} \cdot z_{PR}}}{2 \cdot z_{PR} \cdot z_{PS}}$

TABLE 4 Torque Summary SUN RING CARRIER Simple Planetary τ_(S)$\frac{\tau_{R}}{\tau_{S}} = \frac{z_{R}}{z_{S}}$$\frac{\tau_{C}}{\tau_{S}} = \frac{z_{R} + z_{S}}{z_{S}}$ CompoundPlanetary τ_(S)$\frac{\tau_{R}}{\tau_{S}} = \frac{z_{R} \cdot z_{PS}}{z_{S} \cdot z_{PR}}$$\frac{\tau_{C}}{\tau_{S}} = \frac{{z_{R} \cdot z_{PS}} + {z_{S} \cdot z_{PR}}}{z_{S} \cdot z_{PR}}$Simple Solar $\frac{\tau_{S}}{\tau_{R}} = \frac{z_{S}}{z_{R}}$ τ_(R)$\frac{\tau_{C}}{\tau_{R}} = \frac{z_{R} + z_{S}}{z_{R}}$ Compound Solar$\frac{\tau_{S}}{\tau_{R}} = \frac{z_{S} \cdot z_{PR}}{z_{R} \cdot z_{PS}}$τ_(R)$\frac{\tau_{C}}{\tau_{R}} = \frac{{z_{R} \cdot z_{PS}} + {z_{S} \cdot z_{PR}}}{z_{R} \cdot z_{PS}}$Simple Star τ_(S) $\frac{\tau_{R}}{\tau_{S}} = \frac{- z_{R}}{z_{S}}$$\frac{\tau_{C}}{\tau_{S}} = \frac{- \left( {z_{R} + z_{S}} \right)}{z_{S}}$Compound Star τ_(S)$\frac{\tau_{R}}{\tau_{S}} = \frac{{- z_{R}} \cdot z_{PS}}{z_{S} \cdot z_{PR}}$$\frac{\tau_{C}}{\tau_{S}} = \frac{- \left( {{z_{R} \cdot z_{PS}} + {z_{S} \cdot z_{PR}}} \right)}{z_{S} \cdot z_{PR}}$

TABLE 5 Power Summary SUN RING CARRIER Simple Planetary τ_(S) · ω_(S)$\frac{\tau_{R} \cdot \omega_{R}}{\tau_{S} \cdot \omega_{S}} = {\frac{z_{R}}{z_{S}} \cdot \omega_{R/S}}$$\frac{\tau_{C} \cdot \omega_{C}}{\tau_{S} \cdot \omega_{S}} = \frac{z_{S} + {\omega_{R/S} \cdot z_{R}}}{z_{S}}$Compound Planetary τ_(S) · ω_(S)$\frac{\tau_{R} \cdot \omega_{R}}{\tau_{S} \cdot \omega_{S}} = {\frac{z_{R} \cdot z_{PS}}{z_{S} \cdot z_{PR}} \cdot \omega_{R/S}}$$\frac{\tau_{C} \cdot \omega_{C}}{\tau_{S} \cdot \omega_{S}} = \frac{{z_{S} \cdot z_{PR}} + {\omega_{R/S} \cdot z_{R} \cdot z_{PS}}}{z_{S} \cdot z_{PR}}$Simple Solar$\frac{\tau_{S} \cdot \omega_{S}}{\tau_{R} \cdot \omega_{R}} = {\frac{z_{S}}{z_{R}} \cdot \omega_{S/R}}$τ_(R) · ω_(R)$\frac{\tau_{C} \cdot \omega_{C}}{\tau_{R} \cdot \omega_{R}} = \frac{z_{R} + {\omega_{S/R} \cdot z_{S}}}{z_{R}}$Compound Solar$\frac{\tau_{S} \cdot \omega_{S}}{\tau_{R} \cdot \omega_{R}} = {\frac{z_{S} \cdot z_{PR}}{z_{R} \cdot z_{PS}} \cdot \omega_{S/R}}$τ_(R) · ω_(R)$\frac{\tau_{C} \cdot \omega_{C}}{\tau_{R} \cdot \omega_{R}} = \frac{{z_{R} \cdot z_{PS}} + {\omega_{S/R} \cdot z_{S} \cdot z_{PR}}}{z_{R} \cdot z_{PS}}$Simple Star τ_(S) · ω_(S)$\frac{\tau_{R} \cdot \omega_{R}}{\tau_{S} \cdot \omega_{S}} = \frac{z_{S} - {\omega_{C/S} \cdot \left( {z_{R} + z_{S}} \right)}}{z_{S}}$$\frac{\tau_{C} \cdot \omega_{C}}{\tau_{S} \cdot \omega_{S}} = {\frac{- \left( {z_{R} + z_{S}} \right)}{z_{S}} \cdot \omega_{C/S}}$Compound Star τ_(S) · ω_(S)$\frac{\tau_{R} \cdot \omega_{R}}{\tau_{S} \cdot \omega_{S}} = \frac{{z_{S} \cdot z_{PR}} - {\omega_{C/S} \cdot \left( {{z_{R} \cdot z_{PS}} + {z_{S} \cdot z_{PR}}} \right)}}{z_{S} \cdot z_{PR}}$$\frac{\tau_{C} \cdot \omega_{C}}{\tau_{S} \cdot \omega_{S}} = {\frac{- \left( {{z_{R} \cdot z_{PS}} + {z_{S} \cdot z_{PR}}} \right)}{z_{S} \cdot z_{PR}} \cdot \omega_{C/S}}$

TABLE 6 Speed Reduction Ratios Using Reactive Power Quotients SIMPLECOMPOUND Planetary$\frac{\omega_{S}}{\omega_{C}} = \frac{z_{R} + z_{S}}{z_{S} \cdot \left( {1 + \frac{\tau_{R} \cdot \omega_{R}}{\tau_{S} \cdot \omega_{S}}} \right)}$$\frac{\omega_{S}}{\omega_{C}} = \frac{{z_{R} \cdot z_{PS}} + {z_{S} \cdot z_{PR}}}{z_{S} \cdot z_{PR} \cdot \left( {1 + \frac{\tau_{R} \cdot \omega_{R}}{\tau_{S} \cdot \omega_{S}}} \right)}$Solar$\frac{\omega_{R}}{\omega_{C}} = \frac{z_{R} + z_{S}}{z_{R} \cdot \left( {1 + \frac{\tau_{S} \cdot \omega_{S}}{\tau_{R} \cdot \omega_{R}}} \right)}$$\frac{\omega_{R}}{\omega_{C}} = \frac{{z_{R} \cdot z_{PS}} + {z_{S} \cdot z_{PR}}}{z_{R} \cdot z_{PS} \cdot \left( {1 + \frac{\tau_{S} \cdot \omega_{S}}{\tau_{R} \cdot \omega_{R}}} \right)}$Star$\frac{\omega_{S}}{\omega_{R}} = \frac{- z_{R}}{z_{S} \cdot \left( {1 + \frac{\tau_{C} \cdot \omega_{C}}{\tau_{S} \cdot \omega_{S}}} \right)}$$\frac{\omega_{S}}{\omega_{R}} = \frac{{- z_{R}} \cdot z_{PS}}{z_{S} \cdot z_{PR} \cdot \left( {1 + \frac{\tau_{C} \cdot \omega_{C}}{\tau_{S} \cdot \omega_{S}}} \right)}$

TABLE 7 Vertical Asymptotes and Speed Reduction Ratio Slopes at OrdinateAxes VERTICAL ASYMPTOTE ORDINATE AXIS SLOPE Simple Planetary$\omega_{R/S} = \frac{- z_{S}}{z_{R}}$${\frac{du}{{d\omega}_{R/S}}}_{\omega_{R/S} = 0} = \frac{{- z_{R}} \cdot \left( {z_{R} + z_{S}} \right)}{z_{S}^{2}}$Compound Planetary$\omega_{R/S} = \frac{{- z_{S}} \cdot z_{PR}}{z_{R} \cdot z_{PS}}$${\frac{du}{{d\omega}_{R/S}}}_{\omega_{R/S} = 0} = \frac{{- z_{R}} \cdot z_{PS} \cdot \left( {{z_{R} \cdot z_{PS}} + {z_{S} \cdot z_{PR}}} \right)}{\left( {z_{S} \cdot z_{PR}} \right)^{2}}$Simple Solar $\omega_{S/R} = \frac{- z_{R}}{z_{S}}$${\frac{du}{{d\omega}_{S/R}}}_{\omega_{S/R} = 0} = \frac{{- z_{S}} \cdot \left( {z_{R} + z_{S}} \right)}{z_{R}^{2}}$Compound Solar$\omega_{S/R} = \frac{{- z_{R}} \cdot z_{PS}}{z_{S} \cdot z_{PR}}$${\frac{du}{{d\omega}_{S/R}}}_{\omega_{S/R} = 0} = \frac{{- z_{S}} \cdot z_{PR} \cdot \left( {{z_{R} \cdot z_{PS}} + {z_{S} \cdot z_{PR}}} \right)}{\left( {z_{R} \cdot z_{PS}} \right)^{2}}$Simple Star $\omega_{C/S} = \frac{z_{S}}{z_{R} + z_{S}}$${\frac{du}{{d\omega}_{C/S}}}_{\omega_{C/S} = 0} = \frac{{- z_{R}} \cdot \left( {z_{R} + z_{S}} \right)}{z_{S}^{2}}$Compound Star$\omega_{C/S} = \frac{z_{S} \cdot z_{PR}}{{z_{R} \cdot z_{PS}} + {z_{S} \cdot z_{PR}}}$${\frac{du}{{d\omega}_{C/S}}}_{\omega_{C/S} = 0} = \frac{{- z_{R}} \cdot z_{PS} \cdot \left( {{z_{R} \cdot z_{PS}} + {z_{S} \cdot z_{PR}}} \right)}{\left( {z_{S} \cdot z_{PR}} \right)^{2}}$

It should be appreciated that all speed reduction ratios can be writtenin the form:

$\begin{matrix}{u = \frac{u_{F}}{1 + \kappa}} & (20)\end{matrix}$

where u_(F) is the fixed reaction member speed ratio specific to theparticular epicyclic arrangement and κ is the reactive power quotient.This is true regardless of whether the epicyclic arrangement isplanetary, solar, star, simple or compound. The reactive power quotientcan be a positive or negative quantity. When κ<0, the speed reductionratio will be larger than that of a gear drive with a fixed reactionmember, and the input drive motor must supply power to both the outputand the reaction motor/generator. When κ>0, the speed reduction ratiowill be smaller than that of a fixed reaction member gear drive, and theoutput will be powered by both the input drive motor and the reactionmotor/generator.

Furthermore, the ratio spread, or the quotient between the maximum andminimum speed reduction ratios will determine the power requirements ofthe reaction motor/generator. If the primary drive motor is one with anarrow operating speed range and demands a large spread between the topand bottom speed ratios, the reactive power requirements will be large,possibly several times larger than that of the primary drive motor. Ifthe primary drive motor has a wide operating speed range the reactivepower requirements will be small. A ratio spread of 2.0 results inprimary and reaction power requirements that are equal. Themotor/generator size can be further reduced by mating it with its ownfixed reaction member gear drive, using traditional methods to determineits required speed reduction ratio.

The selection of which type of epicyclic arrangement is optimum (i.e.,planetary, solar or star) depends on the details and the required speedreduction ratio and ratio spread of the application. The slope of thespeed reduction ratio at the ordinate axis of the star arrangement isequal to that of the planetary arrangement and the vertical asymptote ofa star arrangement will always occur at a lower reaction member speed tothat of a planetary arrangement.

Furthermore, the foregoing discussion discloses and describes merelyexemplary embodiments of the present disclosure. One skilled in the artwill readily recognize from such discussion, and from the accompanyingdrawings and claims, that various changes, modifications and variationsmay be made therein without departing from the spirit and scope of thedisclosure as defined in the following claims.

What is claimed is:
 1. A continuously variable transmission for use in amotor vehicle having a prime mover and a driveline driving a pair ofwheels, the transmission comprising: a compound solar epicyclic gearsetincluding a ring gear adapted to be driven by the prime mover, firstpinion gears driven by the ring gear, a sun gear driving second piniongears, and a carrier adapted for driving the driveline; a reaction motordriving the sun gear; and a controller for controlling the reactionmotor to vary the speed of the sun gear and define a gear ratio betweenthe ring gear and the carrier based on the sun gear speed, wherein avertical asymptote of a ratio of carrier speed to sun gear speed versusa ratio of sun gear speed to ring gear speed for the compound solarepicyclic gearset ranges between 5 and
 28. 2. The transmission of claim1 wherein the first pinion gears and the second pinion gears definecompound pinion gears supported by the carrier.
 3. The transmission ofclaim 1 wherein a fixed ring speed ratio of the compound solar epicyclicgearset ranges between 1.03 and 1.25.
 4. The transmission of claim 2being operable in a neutral mode wherein the carrier is not rotatingwhen the ring gear and sun gear are rotating.
 5. The transmission ofclaim 1 further comprising: a first input shaft coupling the prime moverto the ring gear; a second input shaft coupling the reaction motor tothe sun gear; and an output shaft coupling the carrier to the driveline.6. The transmission of claim 1 wherein the output shaft isconcentrically arranged with the second input shaft.
 7. The transmissionof claim 1 wherein the second input shaft coaxially extends with thefirst input shaft.
 8. The transmission of claim 1 further including areduction gearset driven by the second input shaft and driving thecarrier.
 9. The transmission of claim 8 wherein the reduction gearsetincludes a drive gear meshed with a driven gear rotating about offsetaxes.
 10. The transmission of claim 8 wherein the reduction gearsetincludes a worm gear fixed for rotation with the second input shaft anda worm wheel driving the sun gear.
 11. The transmission of claim 8wherein the reduction gearset includes a planetary gearset and furtherwherein the second input shaft, the first input shaft and the outputshaft rotate about a common axis.
 12. A continuously variabletransmission for use in a motor vehicle having a prime mover and adriveline driving a pair of wheels, the transmission comprising: acompound star epicyclic gearset including a sun gear driven by the primemover, first pinion gears meshed with the sun gear, second pinion gearsmeshed with a ring gear, and a carrier rotatably supporting the firstand second pinion gears, the ring gear driving the driveline; a reactionmotor driving the carrier; and a controller for controlling the reactionmotor to vary the speed of the carrier and define a gear ratio betweenthe sun gear and the ring gear based on the carrier speed, wherein avertical asymptote of a ratio of ring gear speed to sun gear speedversus a ratio of carrier speed to sun gear speed for the compound starepicyclic gearset ranges between 0.02 and 0.20.
 13. The transmission ofclaim 12 wherein the first and second pinion gears define a set ofcompound pinion gears.
 14. The transmission of claim 12 wherein a fixedcarrier speed ratio of the compound star epicyclic gearset rangesbetween −4.0 and −28.0.
 15. The transmission of claim 12 furthercomprising: a first input shaft coupling the prime mover to the sungear; a second input shaft coupling the reaction motor to the carrier;and an output shaft coupling the ring gear to the driveline.
 16. Thetransmission of claim 15 wherein the transmission is operable in aneutral mode where the output shaft is not rotating when the first andsecond input shafts are rotating.
 17. The transmission of claim 15wherein the output shaft is concentrically arranged with the secondinput shaft.
 18. The transmission of claim 15 wherein the second inputshaft coaxially extends with the first input shaft.
 19. The transmissionof claim 15 further including a reduction gearset driven by the secondinput shaft and driving the carrier.
 20. The transmission of claim 15wherein the first input shaft is rotated in an opposite direction to theoutput shaft.
 21. A continuously variable transmission for use in amotor vehicle having a prime mover and a driveline driving a pair ofwheels, the transmission comprising: a first input shaft driven by theprime mover; a second input shaft driven by a reaction motor; an outputshaft driving the driveline; and a compound epicyclic gearset includinga ring gear driven by the first output shaft, a sun gear driven by thesecond output shaft, a carrier driving the output shaft, and compoundpinion gears supported by the carrier and meshed with the ring gear andthe sun gear; wherein the reaction motor is operable to vary the speedof the second output shaft to establish a gear ratio between the firstinput shaft and the output shaft based on the speed of the second outputshaft, wherein a vertical asymptote of a ratio of carrier speed to sungear speed versus a ratio of sun gear speed to ring gear speed rangesbetween 5 and
 28. 22. The transmission of claim 21 wherein a fixed ringspeed ratio of the compound epicyclic gearset ranges between 1.03 and1.25.
 23. A continuously variable transmission of use in a motor vehiclehaving a prime mover and a driveline driving a pair of wheels, thetransmission comprising: a first input shaft driven by the prime mover;a second input shaft driven by a reaction motor; an output shaft drivingthe driveline; and a compound epicyclic gearset including a sun geardriven by the first input shaft, a carrier driven by the second inputshaft, a ring gear driving the output shaft, and compound pinion gearssupported by the carrier and meshed with the sun gear and the ring gear;wherein the reaction motor is operable to vary the speed of the secondinput shaft to establish a gear ratio between the first input shaft andthe output shaft based on the speed of the second input shaft, wherein avertical asymptote of a ratio of ring gear speed to sun gear speedversus a ratio of carrier speed to sun gear speed ranges between 0.02and 0.20.
 24. The transmission of claim 25 wherein a fixed carrier speedratio of the compound epicyclic gearset ranges between −4.0 and −28.0.